VASP Computing Ideal Shear Strength of Au

VASP: Ideal Shear Strength of Au

Input files

Here are the basic input files required for VASP calculation. Some of the files need to be changed since we need to perform a large number of calculations.

INCAR

System = fcc Au
LWAVE = .FALSE.
ENCUT  =  400
ISMEAR  = 1
SIGMA = 0.2
ISIF = 2

To increase plane wave cutoff, we manually put PREC = HIGH or PREC = Accurate. Default value is PREC = Medium

KPOINTS

43x43x43
0        0 = automatic generation of k-points
Monkhorst
43 43 43
0 0 0

POSCAR

POSCAR for FCC Au (created by tcl)
4.0615
 0.612372435696  0.000000000000 -0.353553390593
 0.408248290464  0.577350269190  0.000000000000
 0.612372435696  0.000000000000  0.353553390593
1
Cartesian  (real coordinates r)
0    0    0

You also need to put the LDA pseudopotential file as POTCAR in this directory.

Results

Perfect crystal

First, we perform a test simulation in which we relax the electrons in a gold perfect crystal.

 qsub vasp.pbs

The vasp.pbs script is listed below.

#!/bin/bash
#PBS -N Au_perf.43.E4.8
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=24:00:00
#PBS -V

### ---------------------------------------
### BEGINNING OF EXECUTION
### ---------------------------------------

echo The master node of this job is `hostname`
echo The working directory is `echo $PBS_O_WORKDIR`
echo This job runs on the following nodes:
echo `cat $PBS_NODEFILE`

ncpu=`cat $PBS_NODEFILE | wc -w`
echo "Number of processors = $ncpu "

### end of information preamble

cd $PBS_O_WORKDIR
echo $PWD
/opt/mpiexec/bin/mpiexec --comm=pmi -np $ncpu ../../../../bin/vasp.caiwei.mva2 >& $PBS_O_WORKDIR/vasp.log

We run this test case on SU-AHPCRC. The calculation takes 160 seconds (on 8 CPUs) to finish. The ground state energy is E = -4.3951 eV.

Shear deformation

Next, we apply shear strain on (111) plane along the [1 -1 0] direction. This coresponds to $\gamma _{xy}$ in our coordinate system. Due to elastic anisotropy, we need to adjust other strain components, so that the only non-zero stress component is $\sigma _{xy}$. Due to the symmetry of this problem, it turns out that we only need to adjust normal strain components.

For each applied strain $\gamma _{xy}$, we need to run a series of VASP calculations to find the strain components that relax all other stress components except $\sigma _{xy}$. After that, $\gamma _{xy}$ is increased a little further and the relaxation is repeated. For each $\gamma _{xy}$, the shear stress $\sigma _{xy}$ at the end of the relaxation is recorded. The ideal shear stress is the maximum recorded value for $\sigma _{xy}$.

The entire calculation is submitted by the following command.

 qsub tcl.pbs

The tcl.pbs script is listed below.

#!/bin/bash
#PBS -N Au_shear.43.E4.rlx
#PBS -j oe
#PBS -l nodes=1:ppn=8,walltime=96:00:00
#PBS -V

### ---------------------------------------
### BEGINNING OF EXECUTION
### ---------------------------------------

echo The master node of this job is `hostname`
echo The working directory is `echo $PBS_O_WORKDIR`
echo This job runs on the following nodes:
echo `cat $PBS_NODEFILE`

ncpu=`cat $PBS_NODEFILE | wc -w`
echo "Number of processors = $ncpu "

### end of information preamble

cd $PBS_O_WORKDIR

echo $PWD

/usr/bin/tclsh shear_rlx.tcl $ncpu

Here is the shear_rlx.tcl script.

The results will be stored in the stress_rlx.dat file. The first column is proportional to the applied shear strain. The second column is the number of iterations for relaxing the normal stress components given this shear strain. In this test case, the maximum number of iteration at each shear strain is 20. Columns 3,4,5 are the normal stresses (in kB, 1kB = 100MPa). Column 6 is the desired shear stress.

We can select the relaxed shear stress value by the following shell command.

grep " 20  " stress_rlx.dat

The data can be plotted by Matlab or Gnuplot to give the following curve. The maximum stress (i.e. the ideal shear strength) is ?? MPa. (To be completed. The data we get is consistent with Ogata et al. PRB 70, 104104, 2004.)